Find the shortest distance from the point P = (2,2,5)
2,712
Hint: Let $u=\langle 2,2,5\rangle$ and $v=\langle 6,5,4\rangle$, and find $\displaystyle d=\frac{u\times v}{v}$.
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Yusha
Updated on August 15, 2022Comments

Yusha 2 months
Find the shortest distance from the point $P = (2,2,5)$ to a point on the line given by $l:(x,y,z) = (6t, 5t, 4t)$
So I've got the matrix that I think it should look like which is
$\begin{bmatrix}6&5&4\\2&2&5\end{bmatrix}$ but what exactly am I solving here

Yusha about 6 yearsThe derivative of $d(t) = 0$

Kaj Hansen about 6 yearsI'm recommending minimizing $f(t) = (d(t))^2$ by first finding $\displaystyle \frac{df}{dt}$.

Yusha about 6 yearsthere is no $f$

Kaj Hansen about 6 yearsI'm just defining it to be the function $(d(t))^2$ for notational convenience.

Yusha about 6 yearsThis is not a calculus class, this is linear algebra. Shouldn't have to use any sort of calculus for this

Kaj Hansen about 6 yearsThat's alright; you don't have to accept my answer, and we can wait on someone else. I believe in having diverse solutions posted nevertheless.